Algebra - Expansion of Brackets

jerick_hartono
Mind Map by , created over 3 years ago

My mind-map on the basics of expanding brackets in algebra.

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jerick_hartono
Created by jerick_hartono over 3 years ago
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Algebra - Expansion of Brackets
1 We don't usually write x (times) in an equation when multiplying, we instead just put the number in front of the bracket. (Example: 3y(4-2y), not 3y x (4-2y)
2 Distributive Law
2.1 a(b+c)
2.1.1 We expand it by multiplying the number outside the bracket with both numbers inside the bracket.
2.2 (a+b)(c+d)
2.2.1 we do this by multiplying by using SLIP.
3 Perfect Squares
3.1 (a+b)^2
3.2 We get our answer by expanding the brackets, and then simplifying it later,
3.2.1 In general:
4 Difference of 2 Squares
4.1 (a+b)(a-b)
4.1.1 Method: We will first have to expand the brackets, which will be a^2 +ab -ab -b^2. We will then need to simplify the terms and it will become a^2 - b^2.
4.2 When we simplify, the two middle terms cancel out.
4.2.1 Examp,e:
5 Simplifying
5.1 We simplify equations by finding the common factors, and then we simplify.
5.2 This is so that we can see the equations in a much easier way.
5.3 Example:
6 Expanding
6.1 Expanding expression with brackets
6.1.1 When there is a negative term outside the bracket, the sign of the multiplied terms change.
6.1.1.1 Example:
6.1.2 To expand, we have to multiply every term inside a bracket by the term outside the bracket.
6.1.2.1 Example:
6.1.3 Expanding brackets and simplifying
6.1.3.1 Sometimes, we need to multiply out brackets then simplify.
6.1.3.1.1 Multiplying out both brackets or terms and collecting like terms.
6.1.3.2 Examples:
6.2 We have to multiply the bracket in order to expand it.
7 We expand expressions by using SLIP